Quantum Cognition

The Power of Distraction: An

Experimental Test of Quantum

Persuasion

Ariane Lambert-Mogiliansky1(B), Adrian Calmettes2, and Herv´ Gonay3

1 Paris School of Economics, 48 boulevard Jourdan, 75014 Paris, France alambert@pse.ens.fr

2 Department of Political Science, The Ohio State University, 2140 Derby Hall,

154 N Oval Mall, Columbus, OH 43210, USA calmettes.1@osu.edu

3 GetQuanty, 54 rue Greneta, 75002 Paris, France herve.gonay@getquanty.com

Abstract. Quantum-like decision theory is by now a well-developed field. We here test the predictions of an application of this approach to persuasion as developed by Danilov and Lambert-Mogiliansky in [6]. One remarkable result entails that in contrast to Bayesian predictions, distraction rather than relevant information has a powerful potential to influence decision-making. We conducted an experiment in the context of donations to NGOs active in the protection of endangered species.

We first tested the quantum incompatibility of two perspectives ‘trust’ and ‘urgency’ in a separate experiment. We next recruited 1371 respondents and divided them into three groups: a control group, a first treatment group and the main treatment group. Our main result is that ‘distracting’ information significantly a ected decision-making: it induced a switch in respondents’ choice as to which project to support compared with the control group. The first treatment group which was provided with compatible information exhibited no di erence compared with the control group. Population variables play no role suggesting that quantum-like indeterminacy may indeed be a basic regularity of the mind. We thus find support for the thesis that the manipulability of people’s decision-making is linked to the quantum indeterminacy of their subjective representations (mental pictures) of the choice alternatives.

Keywords: Persuasion · Distraction · Information processing · Belief updating · Quantum cognition

1 Introduction

The theory of persuasion was initiated by Kamenica and Gentzkow [12] and further developed in a variety of directions. The subject matter of the theory of persuasion is the use of an information structure (or measurement) that generates new information in order to modify a person’s state of beliefs with the intent

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B. Coecke and A. Lambert-Mogiliansky (Eds.): QI 2018, LNCS 11690, pp. 25–38, 2019. https://doi.org/10.1007/978-3-030-35895-2_2

26 A. Lambert-Mogiliansky et al.

of making her act in a specific way. The question of interest is how much can a person, call him Sender, influence another one, call her Receiver, by selecting a suitable measurement and revealing its outcome. An example is in lobbying. A pharmaceutical company commissions to a scientific laboratory a specific study of a drug impact, the result of which is delivered to the politician. The question of interest from a persuasion point of view is what kind of study best serves the company’s interest.

Receiver’s decision to act depends on her beliefs about the world. In [12] and related works, the beliefs are given as a probability distribution over a set of states of the world. A central assumption is that uncertainty is formulated in the standard classical framework. As a consequence the updating of Receiver’s beliefs follows Bayes’ rule.

However as amply documented the functioning of the mind is more complex and people often do not follow Bayes rule. Cognitive sciences propose alternatives to Bayesianism. One avenue of research within cognitive sciences appeals to the formalism of quantum mechanics (QM). A main reason is that QM has properties that reminds of the paradoxical phenomena exhibited in human cognition. As argued by Danilov and Lambert-Mogiliansky in [6], there also exists deeper reasons for turning to quantum mechanics when studying human behavior. Moreover cognition has been successful in explaining a wide variety of behavioral phenomena such as disjunction e ect, cognitive dissonance, order e ects or preference reversal (see [3, 10]). Finally, there exists by now a fully developed decision theory relying on the principle of quantum cognition (see [7]). Clearly, the mind is likely to be even more complex than a quantum system but our view is that the quantum cognitive approach already delivers interesting new insights in particular with respect to persuasion.

In quantum cognition, the system of interest is the decision-maker’s mental representation of the world. It is represented by a cognitive state. This repre-

sentation of the world is modelled as a quantum-like system so the decision relevant uncertainty is of non-classical (quantum) nature. This modelling approach allows capturing widespread cognitive di culties that people exhibit when constructing a mental representation of a ‘complex’ alternative (cf, [4]). The key quantum property that we use is that some characteristics (cf. properties) of a complex mental object may be “Bohr complementary” that is incompatible in the decision-maker’s mind: she cannot combine in a stable way pieces of information from the two perspectives. A central implication is that measurements (new information) modifies the cognitive state in a non-Bayesian well-defined manner.

As in the classical context our rational Receiver uses new information to update her beliefs so that choices based on updated preferences are consistent with ex-ante preferences defined for the condition (event) that triggered updating. In [7], we learned that a dynamically consistent rational quantum-like decision-maker updates her beliefs according to the von Neumann-L¨uders postulate. In two recent papers, important theoretical results were established. First, as shown in [5], in the absence of any constraints on measurements, full persuasion applies: Sender can always persuade Receiver to believe anything that favors

him. Next, in [6] the same authors investigate a short sequence of measurements but in the frame of a simpler task that they call “targeting”. The object of “targeting” is the transition of a belief state into another specified target state. The main results of relevance to our issue is that distraction providing ‘not relevant’ or ‘incompatible’ information has significant persuasion power. This is in sharp contrast with the Bayesian context where such information should have minimal or no e ect at all.

The present paper aims at testing experimentally those predictions. More precisely, we want to test whether a question (a measurement) addressing a perspective that is incompatible with the information relevant for the decision at stake can a ect decision-making. That is we test the concluding statement in Akerlof and Shiller’s book (see [1]) “just change the focus of people’s mind and you change the decisions they make”.

In the psychology literature, the distraction e ect was first introduced by Festinger and Maccoby in [9]. Its link with persuasion has now proved empirically valid through many di erent experimental contexts (for a review, [2]).1 Interestingly studies (see [16]) have shown how a noninformative signal can decrease documented resistance to persuasion (see [8]). In addition, across five di erent experimental contexts and content domains, Kupor and Tormala revealed in [14] that interruptions that temporarily disrupt(distract) a persuasive message can increase consumers’ processing of that message; consumers being more persuaded by interrupted messages than they would be by the exact same messages delivered uninterrupted.

The situation that we consider is the following. People are invited to choose between two projects aimed at saving endangered species (Elephants and Tigers). The selected project will receive a donation of 50e(one randomly selected respondent will determine the choice). We consider two perspectives of relevance for the choice: the urgency of the cause and the trustworthiness (or honesty) of the organization that manages the donations. As a first step, in a separate experiment we establish that the two perspectives are incompatible by exhibiting a significant order e ect (as in [3, 17]. In the main experiment, respondents were divided into three groups: a control and two treatment groups. They all go through a presentation of the projects and some questions about their preferences. The di erence between the groups is that the first treatment group receives general additional information compatible with their (elicited) preferences while the second one receives general additional information incompatible with their preferences.

The results are in accordance with the predictions of the theoretical model: incompatible information has a significant impact such that the respondents on the whole switched their choice as compared with the control. Compatible

1Decades of research on social influence have emphasized two distinct routes to persuasion: the “central” route and the “peripheral” route. According to Petty and Cacioppo in [16], the central route involves influence that takes place as a result of relatively deep processing of information that is high in message relevance, whereas the peripheral route involves influence that takes place as a result of relatively superficial processing of information that is low in message relevance.